Homoclinic solutions of an infinite-dimensional Hamiltonian system
Homoclinic solutions of an infinite-dimensional Hamiltonian system
复制标题
DOI：
10.1007/s002090100383
复制
发表时间：
2002-06
影响因子：
0.8
通讯作者：
T. Bartsch;Yanheng Ding
中科院分区：
文献类型：
--
作者：
T. Bartsch;Yanheng Ding
我们考虑系统\begin{equation*} \left\{ \begin{array}{l} \partial_t u-\Delta_x u+V(x)u = H_v(t,x,u,v) [3mm] -\partial_t v-\Delta_x v+V(x)v = H_u(t,x,u,v) \end{array}\qquad\text{for }(t,x)\in{\mathbb R}\times{\mathbb R}^N \right. \end{equation*}它是一个无界哈密顿系统。我们假设常数函数是平稳解，并且在变量中是周期性的。为了得到满足条件的同斜解z=(u,v)，我们提出了一个变分公式。允许v改变符号，允许基本谱低于（或高于）0。我们还处理了有界域的情况，而不是用狄利克雷边界条件。
We consider the system\begin{equation*} \left\{ \begin{array}{l} \partial_t u-\Delta_x u+V(x)u = H_v(t,x,u,v) [3mm] -\partial_t v-\Delta_x v+V(x)v = H_u(t,x,u,v) \end{array}\qquad\text{for }(t,x)\in{\mathbb R}\times{\mathbb R}^N \right. \end{equation*}which is an unbounded Hamiltonian system in. We assume that the constant functionis a stationary solution, and thatHandVare periodic in thetandxvariables. We present a variational formulation in order to obtain homoclinic solutionsz=(u,v) satisfyingas. It is allowed thatVchanges sign and thathas essential spectrum below (and above) 0. We also treat the case of a bounded domaininstead ofwith Dirichlet boundary conditions.